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Chapter 1: Q. 104 (page 16)

In Problems 101鈥�104, find the length of each side of the triangle determined by the three points P1 , P2 , and P3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)

P1=7,2,P2=-4,0,P3=4,6

Short Answer

Expert verified

The length of sides of triangle are 5,10and55.

The triangle is a Right Triangle.

Step by step solution

01

Step 1. Given Information

P1=7,2,P2=-4,0,P3=4,6

02

Step 2. Distance Between P1 and P2

dP1,P2=7+42+2-02=125=55

03

Step 3. Distance between P2 and P3

dP2,P3=-4-42+0-62=100=10

04

Step 4. Distance between P1 and P3

dP1,P3=7-42+2-62=25=5

05

Step 5. Check for Right Triangle

52+102=55225+100=125

The equation is true, the triangle is a right triangle.

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Most popular questions from this chapter

The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph?

(a)y-2x=2y+2x=-1(b)y-2x=02y+x=0(c)2y-x=22y+x=-2(d)y-2x=2x+2y=-1(e)2x+y=-22y+x=-2

Find the midpoint of the line segment joining the points P1 and P2 .

P1=(-5,-3);P2=(11,9)

The equation 2x-y=Cdefines a family of lines, one line for each value of C. On one set of coordinate axes, graph the members of the family when C=-4,C=0and C=2. Can you draw a conclusion from the graph about each member of the family?

Graph the line containing the point P and having slope m.

P(1,3),m=-25

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends \(40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends \)60,000, then 200,000 boxes will be sold.

(a) Write a linear equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

(b) How much advertising is needed to sell 300,000 boxes of cereal?

(c) Interpret the slope.
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